Nonlinear Analysis of Airfoil Flutter at Transonic Speeds

摘要

Hopf-bifurcation analysis is used to determine flutter boundaries of a pitch andplunge airfoil (PAPA) at transonic Mach number conditions. The PAPA model is a coupling of the Euler equations and a two-degree-of-freedom structural model composed of linear and torsional springs. The Euler equations are discretized using an upwind total variation diminishing scheme (TVD) of Harten and Yee. Equilibrium solutions of the PAPA model are computed using Newton's method and dynamic solutions are explicitly integrated in time with first-order accuracy. The Hopf-bifurcation point, which models the flutter condition, is computed directly by solving an extended system of equilibrium equations following the approach of Griewank and Reddien. The extended system is solved using a blocked Gauss-Seidel Newton relaxation scheme to improve computational resource requirements.